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On Calibrating Stochastic Volatility Models with time-dependent Parameters
Calibrating Stochastic Volatility Models time-dependent Parameters
2010/10/22
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical resu...
Density quantization method in the optimal portfolio choice with partial observation of stochastic volatility
Optimal portfolio partial observation ltering density
2010/10/21
Computational aspects of the optimal consumption and investment with the partially observed stochastic volatility of the asset prices are considered. The new quantization approach to filtering - dens...
Analytical and Numerical Approaches to Pricing the Path-Dependent Options with Stochastic Volatility
Analytical Numerical Pricing Path-Dependent Options Stochastic Volatility
2010/10/21
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. Fo...
Small-time asymptotics for fast mean-reverting stochastic volatility models
Small-time asymptotics fast mean-reverting stochastic volatility models
2010/10/21
In this paper, we study stochastic volatility models in regimes where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the...
A contribution to the systematics of stochastic volatility models
fluctuations econophysics stochastic differential equations
2010/10/21
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail,...
Valuation equations for stochastic volatility models
Valuation equations stochastic volatility models
2010/10/20
We study the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models. The standard Feynman-Kac theorem cannot be directly applied ...
A Fast Mean-Reverting Correction to Heston's Stochastic Volatility Model
Stochastic volatility Heston model fast mean-reversion
2010/10/21
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is...
Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models
Spectral Decomposition Option Prices Fast Mean-Reverting Stochastic Volatility Models
2010/10/21
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatilit...
Moment Explosions and Long-Term Behavior of Affine Stochastic Volatility Models
Moment Explosions Long-Term Behavior Affine Stochastic Volatility Models
2010/12/13
We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the sense of Duffie, Filipovic and Schachermayer [20...
Multivariate stochastic volatility using state space models
Multivariate stochastic volatility state space models
2010/12/13
A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distrib...